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\author{Derek Lontine}
\title{Statement of Purpose}\label{key}
\begin{document}
\LARGE{US Synthetic / UofU CSM Update}

\LARGE{\textit{Derek Lontine}}\\[.25in]


\normalsize
The intent of this document is to detail the US Synthetic approved projects that have been vetted. Also, this document details a proposed schedule, expected courses, etc.

Over the last several weeks, I have been meeting with members of the executive staff, and other engineering leadership at US Synthetic. I have formed a panel at US Synthetic that will advise and review my progress in pursuing a masters degree. This panel consists of the following:
\begin{itemize}
\item \textbf{Ken Bertagnolli} - VP Research and Development
\item \textbf{Scott Schmidt} - VP Engineering
\item \textbf{Trent Butcher} - General Legal Counsel
\item \textbf{Kevin Graham} - Engineering Manager
\end{itemize}


This panel has convened several times to review potential research options and what their impact is on US Synthetic and my skill development. We have discussed the options at length and vetted them. The vetting process for the projects asked three main questions:
\begin{itemize}
\item What unique skills will be developed in pursuing the particular thesis option?
\item Is this research of great enough value to US Synthetic to justify summer support for advisor?
\item Will pursuing and publishing findings of this research put US Synthetic at risk 
\end{itemize}

The results of these meetings have been quite fruitful. There is common consensus that the research is of great importance, and that having me seek a graduate degree is in the best interest of me and the company. There is also consensus that the CSM group is best suited to help develop the skills needed to be successful in developing computational models for ultra high-pressure research. We also found that the best course of action would be to seek a MS degree with a thesis. It is in this way that I can maximize my involvement with you and your team and learn more. 

\pagebreak
\section{Approved Projects}

The proposed projects are as follows:
\begin{enumerate}
\item Calibration of material model of MgO and boron epoxy at very high quasi-static pressures ($>$5 GPa)
\item Simple systems to produce stress paths similar to those observed in HPHT cubic presses
\item Multi-scale modeling of cobalt cemented tungsten carbide plasticity and fracture
\item Influence of seed fractures and initiation of other fracture of material and it's influence in setting geometry for HPHT systems
\end{enumerate}

\subsection{Calibration of Material Model of MgO or boron epoxy at very high quasi-static pressures ($>$5GPa)}

Material properties at ultra high pressures are relatively difficult to interrogate. Traditional methods to obtain quasi-static pressures $>$5GPa employ extreme stress gradients to drive pressure up in a localized central region of the apparatus. Some of the geometries used to generate these pressures are:
\begin{itemize}
\item Diamond Anvil Cells % (2 opposed anvils)
\item The Bridgman Anvil Cell % (2 opposed anvils)
\item The Toroidal Anvil Cell % (2 opposed anvils)
%\item HPHT Belt Press (2 opposed anvils with confining ring)
%\item Tetrahedral Press (4 anvils)
%\item Cubic Press (6 anvils)
%\item Octahedral Press (8 anvils)
\end{itemize}

The geometry in theses cases is typically axisymmetric. A brief search of the above keywords will reveal a great deal of literature on these systems. Most of the research I have investigated centers on generating higher pressures, interrogating microstructure effects, and some simple stress analyses. 

A more detailed analysis of the complete behavior of the material is desired. The end objective being to simulate the behavior of material properties in the bridgman anvil. The hypothesis is if we can simulate material behavior on more simple cases (such as a bridgman anvil), then simulation of more complex geometries may be simulated accordingly.

At US Synthetic we do not use MgO or Boron Epoxy as our pressure transmission or gasketing medium. We have a proprietary material that USS does not feel comfortable publishing data on. The benefit to USS for this work is that we are able to learn how to test our materials, and then duplicate this work for our proprietary materials.

\subsection{Simple systems to produce stress paths similar to those observed in HPHT cubic presses}

In addition to some of the high pressure systems mentioned above, there are other high pressure configurations called "large volume" high pressure apparatuses. These types of systems are primarily used for manufacturing where the "small volume" are traditionally used in the research community. The trouble with large volume apparatuses is that the cost, geometry, measurements systems and stress state can be fairly complicated. Creating simple high pressure apparatuses can help to probe some of the more complicated stress states without the other negative impacts.

In many regards, this project is very similar to the first project. The differentiation is investigating novel geometries to probe stress states of materials as opposed to calibrating a material model using existing systems. In the ultra high pressure world there are relatively few number of loading systems. There is evidence to suggest that the stress states in traditional cases may not accurately simulate behavior achieved in large volume high pressure apparatuses.

\subsection{Multi-scale modeling of cobalt cemented tungsten carbide plasticity and fracture}

We have made observations on many of our machine tools made from tungsten carbide that there are large amounts of plastic deformation. For example in a 5x5" cemented tungsten carbide tool, USS has observed plastic deformation of about 0.040" (0.8 percent strain). Upon sectioning these materials and investigating them under SEM, we have observed deformation of the cobalt binder. 

Improved analysis of these WC tools can yield useful information regarding the proper design and synthesis of these tools. A multi-scale model may greatly enhance that learning.

There has been some literature on and work performed relative to multi-scale modeling of cemented tungsten carbide. For example \href{http://publications.lib.chalmers.se/records/fulltext/179635/179635.pdf}{Chalmers} 
executed some work on multi-scale modeling of tungsten carbide, however, it seems to me that he treated WC very similar to polycrystalline steel. A detailed analysis of interactions between the cobalt and tungsten carbide, cobalt pooling effects, and porosity may be useful to enhancing a model of tungsten carbide.

\subsection{Influence of seed fractures and initiation of other fracture of material and it's influence in setting geometry for HPHT systems}

One of the problems that plagues HPHT systems is the random nature at which the pressure medium (traditionally pyrophyllite) initially fails and flows. My colleagues and I have found that one of the most critical aspects of the HPHT process is the very first failure of the pyrophyllite. In some cases, the material will get crushed and large regions can spall, creating a great deal of variation in the HPHT process from one run to another.

Another piece of information that we have discovered is the existence of "seed fractures" in our pressure medium. Using a CT scan, we found random fractures that exist in the material before they are run in the HPHT process. These fractures could contribute to the variation in the initial flow and spallation of the pyrophyllite. 

The MPM should be a great method to investigate this behavior. Research into the quantity and random orientation of the seed fractures and how they set initial geometry of a failed component can be very useful.

\definecolor{Gray}{gray}{0.9}

\section{Proposed Schedule}

The following schedule is one of many proposed to meet the requirements of the degree. The pace of this schedule is relatively slow, primarily because of my full time employment at US Synthetic.

\begin{tabular}{|c|c|c|c|}
\rowcolor{Gray}
\hline \textbf{Date/Term} & \textbf{Description} & \textbf{Course Cred} & \textbf{Thesis Cred} \\ 
\hline Spring 2015 & Non-Matriculated & 3 &  \\ 
\hline Summer 2015 & Non-Matriculated & 3 &  \\ 
\hline Fall 2015 &  & 3 &  \\ 
\hline Spring 2016 &  & 3 & 3 \\ 
\hline Summer 2016 &  & 3 & 3 \\ 
\hline Fall 2016 &  & 3 & 3 \\ 
\hline Spring 2017 &  & 3 &  \\ 
\hline May 2017 & Graduate &  &  \\ 
\hline 
\end{tabular} 


\pagebreak
\section{Expected Courses}

The following is a list of courses that I expect will aid me in developing skills. These skills will help me to be successful in completing the thesis and also becoming a more competent engineer. I plan on taking 7 of the 8 courses listed below:

\begin{enumerate}
\item ME EN 6510- Introduction to Finite Elements
\item ME EN 6300- Advanced Strength of Materials
\item ME EN 6500- Engineering Elasticicy
\item ME EN 6530- Introduction to Continuum Mechanics
\item ME EN 7540- Advanced Finite Elements
\item ME EN 7530- Fundamentals of Fracture Mechanics
\item MATH 6790- Computational Engineering and Science
\item MATH 6760- Continuum Mechanics: Solids

\end{enumerate}


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